Smoked or grilled over indirect heat? Low and slow gives wonderful results. The downside? No braising liquid for the potatoes, carrots and cabbage. For traditional corned beef and cabbage, I say braise.

Ross yes, some of it is over brined. I was thinking braising it the same way we normally do bristket would make it quite nice.

I brine my own, so I guess I don't how a piece of meat can over brine unless the processed stuff uses too much salt. Mine brines for over a month, yet the meat is not overly salty.
I have always braised. Cabbage and potatoes cooked separately.